In a previous work [1] we introduced a construction designed to produce biorthogonal multiresolutions from given subdivisions. This construction was formulated in matrix terms, which is appropriate for curves and tensor-product surfaces. For mesh surfaces of non-tensor connectivity, however, matrix notation is inconvenient. This work introduces diagrams and diagram interactions to replace matri...

In this correspondence, we generalize the theory of compactly supported biorthogonal two-channel wavelet bases to M -channel. A sufficient condition for the M -channel perfect reconstruction filter banks to constructM -channel biorthogonal bases of compactly supported wavelets is derived. It is shown that the construction of biorthogonal M -channel wavelet bases is equivalent to the design of a...

New lapped transforms are introduced. The LBT (lapped biorthogonal transform), and HLBT (hierarchical lapped biorthogonal transform) are appropriate for image coding, and the MLBT (modulated lapped biorthogonal transform) and NMLBT (nonuniform modulated lapped biorthogonal transform) are appropriate for audio coding. The HLBT has a significantly lower computational complexity than the LOT (lapp...

In [1], Beylkin et al. introduced a wavelet-based algorithm that approximates integral or matrix operators of a certain type by highly sparse matrices, as the basis for efficient approximate calculations. The wavelets best suited for achieving the highest possible compression with this algorithm are Daubechies wavelets, while Coiflets lead to a faster decomposition algorithm at slightly lesser ...

An algebraic approach to the design of different binds of discrete wavelet transforma (orthogonal and biorthogonal single-/multiwavelet transforms, multiwavelet-like transforma) is taken. The different transfomrs are anaL ysed with respect to computational efforts, approzimation properties and symmetry. The design of the orthogonal and biorthogonal single-/multiwavelets requires the solution of...

We use generating functions to express orthogonality relations in the form of q-beta integrals. The integrand of such a q-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegő and leads naturally to the Al-Salam-Chihara p...